The present invention relates to a filtering system and more particularly to an equalization system and method for utilizing adaptive digital filters with non-linear frequency resolution.
Quality audio products are designed with the goal of reproducing as accurately as possible at the listener's ears the acoustic signal originally recorded or broadcast. Yet despite the many improvements that have been made in audio technology in the past several years, there still remains at least one major obstacle to achieving that goal.
Room boundaries can have a significant effect on the sound radiated by a loudspeaker and eventually perceived by the listener. Reflections off walls and furniture combine at the listener's ears in a complex manner such that the various frequency components in the music are unbalanced, influencing the sound to a greater extent than any other component in the system. The problem is difficult to deal with because the extent of the problem can only be assessed by making a measurement of the system at the exact listening position.
A solution to the problem is to use adaptive digital filters to develop inverse filters for the loudspeaker/room response. The invertability of these system responses has been studied and numerous solutions have been proposed. Several of these solutions involve frequency domain transform techniques to design finite impulse response ("FIR") filters. Various configurations of time domain adaptive FIR filters have also been developed. Although adaptive infinite impulse response ("IIR") filters are also applicable, problems of convergence and stability generally make them less practical.
In most systems using inverse filters for equalization, one or more loudspeakers are located in a small to medium sized room such as a studio control room or domestic living room. During a separate calibration mode, a test signal is output through a loudspeaker and received at a microphone, located near, but by necessity not coincident to, the location of the listener's ears. Inverse filter coefficients are then generated from the measured transfer function. These coefficients are then transferred to a fixed digital filter for use in the playback mode, at which time the system processes the audio source material in real time.
Frequency response anomalies in a room are the results of the reinforcement and cancellation which occur when sound waves from various sources (i.e., direct and reflected) add together in and out of phase. It has been found that the average distance between pressure maxima in a room is about 0.9 times the wavelength. It follows that the level of high frequency sounds, with short wavelengths, will vary significantly between nearby points, while that of the longer wavelength low frequencies will be less position sensitive.
This issue is generally ignored in applying equalization, but becomes extremely important as the resolution and accuracy of the inverse correction filter improves. Since a listener must use two ears, generally separated by about 20 cm, it is not physically possible to provide perfect equalization across the full audio band at both ears simultaneously. This clearly suggests that while low frequencies may be corrected quite accurately, higher frequencies must be treated differently.
To further complicate the issue, the auditory system has the ability to discriminate direct sound from later reflections, as well as the ability to detect the direction from which a sound is coming. It also perceives tones on a logarithmic frequency scale, rather than the linear range in which adaptive filters operate. While the ability to generate very accurate equalization filters is one of the goals of the known adaptive systems, i.e., minimize an error in the least mean squared sense, it is not necessarily correct from psychoacoustic criteria.
From the above discussions, it is clear that improvements over the current state of the art require a means for more effectively controlling filter accuracy as a function of frequency and space. Existing techniques approach the problem by either controlling the resolution of the filter directly, as in U.S. Pat. No. 4,628,530 to Philips, or with a multi-band approach, using high resolution digital filters for low frequencies, and low resolution analog or digital filters at high frequencies. Current means of implementing this multi-band approach require that the signal to be equalized be split into two or more frequency bands and operated on by parallel filters. This has several disadvantages. First, since there is no interaction between the filters in the various bands, it makes the adaptation of the filters difficult. Secondly, the additional processing steps of band splitting and recombination distort the signal and introduce noise into the system.
Referring to FIG. 1, the basic structure of a known adaptive FIR filter is shown. The output of the filter y(n) is the linear combination of current and delayed signal values x(n-i) scaled by the filter coefficients ai, where 0.ltoreq.i.ltoreq.N-1, with N being the number of signal values, i.e. EQU y(n)=a.sub.0 x(n)+a.sub.1 x(n-1)+. . . +a.sub.N-1 x(n-N+1)
The filter coefficients a0 to aN-1 are updated based on an error signal e(n), which is the difference between the filter's output y(n) and a reference signal d(n). Any known method may be used for performing this update including those described in "Adaptive Signal Processing", edited by L. H. Sibul, 1987 IEEE Press, New York. Such known methods typically attempt to minimize some function of the error signal e(n). The coefficient update equation for the LMS algorithm is (with K being the convergence factor): EQU a.sub.i (n+1)=a.sub.i (n)+K e(n) x(n-i)
By choosing an appropriate input and reference signal, this technique can be used to adaptively design digital filters with responses matched to the given signals.
FIG. 2 illustrates a predictive filter structure used for equalization, which is described in U.S. Pat. No. 4,458,362 issued to Berkovitz et al. Here the filter A(n) is updated based on the error between the current input signal sample and its predicted value y(n). If x(n) is the output of a system driven by a "white" sequence, it can be shown that the resulting filter is an inverse of the system response, with properties suitable for use as an equalizer.
A digital filter's frequency resolution is directly proportional to its length. If we define resolution to be the minimum 3 dB feature bandwidth, and assume that an adapted FIR filter represents a rectangularly windowed version of an optimal Infinite Impulse Response (IIR) filter, then EQU f.sub.res =0.89.times.f.sub.s /N
where fres is the resolution in Hertz, f.sub.s is the sampling frequency in Hertz, and N is the total number of FIR filter coefficients.
For high quality audio applications, a common sampling frequency is 44,100 H.sub.z. For the filter to have better than 20 H.sub.z resolution, which would be needed for satisfactory equalization at low frequencies, N must be greater than 1960. However, in typical audio applications, this resolution is required only at very low frequencies, which is a small fraction of the total signal bandwidth f.sub.s /2. For most adaptive algorithms such a long filter introduces computational difficulties. In the case of algorithms such as the LMS, the problem is one of convergence and "misadjustment" due to algorithm noise. This leads to a significant disparity between the adaptive filter and the theoretical optimal filter.
It is therefore a principal object of the present invention to provide inverse filters whose accuracy can be controlled as a function of frequency.
An additional object of this invention is to provide a method for accurately adapting an FIR filter when a large number of filter taps are required to obtain adequate frequency resolution.
Yet another object of this invention is to provide an efficient means for implementing long FIR filters which do not introduce amplitude or phase distortions into the response by band splitting and recombination.